Chapter 2: Q5P (page 74)

Evaluate each of the following in x+yform, and compare with a computer solution.
$l n (- \sqrt{2} i - \sqrt{2})$

Short Answer

Expert verified

Theform of the given equation $l n (- \sqrt{2} i - \sqrt{2})$ is, $\ln (2) + (\frac{5 π}{4 + 2 n π} 4 + 2 n π) i .$ .

Step by step solution

Given Information.

The given expression is, $l n (- \sqrt{2} i - \sqrt{2})$ .

Meaning of rectangular form.

Represent the complex number in rectangular form means writing the given complex number in the form of x+iy in which is x the real part and y is the imaginary part.

Convert in polar form.

Consider $z = - \sqrt{2} - i \sqrt{2 .}$

Write the polar form of the number.

$z = r e^{(i θ)}$

The angle is located in second quadrant so the angle must be accordingly.

$r = |- \sqrt{2} i - \sqrt{2}| r = 2 θ = π + \frac{π}{4} θ = \frac{5 π}{4}$

Put the values in the polar form.

$z = 2 e^{(\frac{5 π}{4})}$

Write in the form of .

Convert the polar form into the rectangular form.

$w = \ln (r^{(θ i)}) w = \ln (r) + (\frac{5 π}{4} + 2 n π) i w = \ln (2) + (\frac{5 π}{4} + 2 n π) i w = \ln (r) + (\frac{5 π}{4} + 2 n π) i w h e r e n = 0, \pm 1, \pm 2, \pm 3, . . .$

Therefore, the form of the given equation $l n (- \sqrt{2} i - \sqrt{2})$ is, $\ln (2) + (\frac{5 π}{4} + 2 n π) i$ .

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Evaluate each of the following in x+yform, and compare with a computer solution.
$l n (- \sqrt{2} i - \sqrt{2})$

Short Answer

Step by step solution

Given Information.

Meaning of rectangular form.

Convert in polar form.

Write in the form of .

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Evaluate each of the following in x+yform, and compare with a computer solution.ln(-2i-2)

Short Answer

Step by step solution

Given Information.

Meaning of rectangular form.

Convert in polar form.

Write in the form of .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Classical Mechanics

Geometrical and Physical Optics

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Study anywhere. Anytime. Across all devices.

Evaluate each of the following in x+yform, and compare with a computer solution.
$l n (- \sqrt{2} i - \sqrt{2})$